WeightedCliqueLifting

WeightedCliqueLifting is a Python class for lifting a weighted-directed graph into a simplicial complex by using Ricci Curvature information on the graph edges. This transformation is useful in topological data analysis, where higher-order interactions are represented by simplicial complexes.

Table of Contents

1. Usage
2. Our New Dataset
3. Our Methods

Usage

To use the WeightedCliqueLifting class, you need to instantiate it and call the lift_topology method with a torch_geometric.data.Data object.

import torch_geometric
from modules.transforms.liftings.graph2simplicial.base import Graph2SimplicialLifting
from your_module import WeightedCliqueLifting

# Instantiate the class
lifting = WeightedCliqueLifting(complex_dim=3)

# Assume `data` is a torch_geometric.data.Data object
lifted_topology = lifting.lift_topology(data)

Please follow the tutorial in tutorials/digraph2simplicial/weighted_clique_lifting.ipynb for an example.

Our New Dataset:

We have added a new dataset for our lifting. This dataset is an Ethereum Token Network exchange graph for September 30, 2023.

The dataset has the following attributes:

• edge_index: The indexes for all edges in the graph
• num_nodes : The number of nodes in the graph
• num_edges: the number of edges in the graph
• features: The node labels for the graph depending on what the node identifies with in the network (assets: 0, derivatives: 1, dex: 2, lending: 3, unknown: 4). Note: most are unknown, there are few nodes not labeled 4
• x: The edge weights used in our calculations explained below. The edge weights are pre-normalized for your convenience. Normalization formula taken from Dissecting Ethereum Blockchain Analytics: What We Learn from Topology and Geometry of Ethereum Graph

The dataset is stored in datasets/Transactions/EthereumTokenNetwork/EthereumTokenNetwork.pt

Our Methods:

To perform our topological lifting from a weighted-directed graph to a simplicial complex we follow the following steps:

1. Import our dataset from torch_geometric and make it into a directed networkx graph object
2. Create a weight hashmap for the graph
3. Calculate the Forman-Ricci Curvature for the edges
4. Update the edge distances using the Forman-Ricci Curvature
5. Remove edges based on the given percentile value in the dataset config file
6. Identify cliques in the graph
7. Create a simplicial complex using the cliques

Who We Are:

Submission Completed by Ronan Buck, Vedant Patel, Guneet Uberoi from The University of Central Florida under the supervision of Cuneyt Gurcan Akcora.

Please reach us at Vedant Patel , Ronan Buck and Guneet Uberoi .

Questions

Feel free to contact us through GitHub issues on this repository, or through the Geometry and Topology in Machine Learning slack. Alternatively, you can contact us via mail at any of these accounts: guillermo.bernardez@upc.edu, lev.telyatnikov@uniroma1.it.